結果
| 問題 | No.732 3PrimeCounting |
| ユーザー |
 uwi
|
| 提出日時 | 2018-09-07 21:43:59 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 902 ms / 3,000 ms |
| コード長 | 11,738 bytes |
| コンパイル時間 | 4,805 ms |
| コンパイル使用メモリ | 90,052 KB |
| 実行使用メモリ | 81,840 KB |
| 最終ジャッジ日時 | 2024-11-29 12:09:37 |
| 合計ジャッジ時間 | 31,776 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 89 |
ソースコード
package contest180907;import java.io.ByteArrayInputStream;import java.io.IOException;import java.io.InputStream;import java.io.PrintWriter;import java.util.Arrays;import java.util.InputMismatchException;public class D {InputStream is;PrintWriter out;String INPUT = "";void solve(){int n = ni();int[] primes = sieveEratosthenes(3*n);long[] a = new long[n+1];for(int p : primes)if(p <= n)a[p] = 1;long[] a2 = convolute(a, a);long[] a3 = convolute(a2, a);long[] am2 = new long[2*n+1];for(int p : primes)if(p <= n)am2[2*p] = 1;long[] am3 = convolute(am2, a);long ret = 0;for(int p : primes) {ret += a3[p] - am3[p] * 3;}out.println(ret/6);}public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441,976224257, 975175681};public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17};// public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793,924844033};// public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5};public static long[] convoluteSimply(long[] a, long[] b, int P, int g){int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);long[] fa = nttmb(a, m, false, P, g);long[] fb = a == b ? fa : nttmb(b, m, false, P, g);for(int i = 0;i < m;i++){fa[i] = fa[i]*fb[i]%P;}return nttmb(fa, m, true, P, g);}public static long[] convolute(long[] a, long[] b){int USE = 2;int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);long[][] fs = new long[USE][];for(int k = 0;k < USE;k++){int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];long[] fa = nttmb(a, m, false, P, g);long[] fb = a == b ? fa : nttmb(b, m, false, P, g);for(int i = 0;i < m;i++){fa[i] = fa[i]*fb[i]%P;}fs[k] = nttmb(fa, m, true, P, g);}int[] mods = Arrays.copyOf(NTTPrimes, USE);long[] gammas = garnerPrepare(mods);int[] buf = new int[USE];for(int i = 0;i < fs[0].length;i++){for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];long[] res = garnerBatch(buf, mods, gammas);long ret = 0;for(int j = res.length-1;j >= 0;j--)ret = ret * mods[j] + res[j];fs[0][i] = ret;}return fs[0];}public static long[] convolute(long[] a, long[] b, int USE, int mod){int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);long[][] fs = new long[USE][];for(int k = 0;k < USE;k++){int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];long[] fa = nttmb(a, m, false, P, g);long[] fb = a == b ? fa : nttmb(b, m, false, P, g);for(int i = 0;i < m;i++){fa[i] = fa[i]*fb[i]%P;}fs[k] = nttmb(fa, m, true, P, g);}int[] mods = Arrays.copyOf(NTTPrimes, USE);long[] gammas = garnerPrepare(mods);int[] buf = new int[USE];for(int i = 0;i < fs[0].length;i++){for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];long[] res = garnerBatch(buf, mods, gammas);long ret = 0;for(int j = res.length-1;j >= 0;j--)ret = (ret * mods[j] + res[j]) % mod;fs[0][i] = ret;}return fs[0];}// static int[] wws = new int[270000]; // outer faster// Modifed Montgomery + Barrettprivate static long[] nttmb(long[] src, int n, boolean inverse, int P, int g){long[] dst = Arrays.copyOf(src, n);int h = Integer.numberOfTrailingZeros(n);long K = Integer.highestOneBit(P)<<1;int H = Long.numberOfTrailingZeros(K)*2;long M = K*K/P;int[] wws = new int[1<<h-1];long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);long w = (1L<<32)%P;for(int k = 0;k < 1<<h-1;k++){wws[k] = (int)w;w = modh(w*dw, M, H, P);}long J = invl(P, 1L<<32);for(int i = 0;i < h;i++){for(int j = 0;j < 1<<i;j++){for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){long u = (dst[s] - dst[t] + 2*P)*wws[k];dst[s] += dst[t];if(dst[s] >= 2*P)dst[s] -= 2*P;// long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;long Q = (u<<32)*J>>>32;dst[t] = (u>>>32)-(Q*P>>>32)+P;}}if(i < h-1){for(int k = 0;k < 1<<h-i-2;k++)wws[k] = wws[k*2];}}for(int i = 0;i < n;i++){if(dst[i] >= P)dst[i] -= P;}for(int i = 0;i < n;i++){int rev = Integer.reverse(i)>>>-h;if(i < rev){long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;}}if(inverse){long in = invl(n, P);for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P);}return dst;}// Modified Shoup + Barrettprivate static long[] nttsb(long[] src, int n, boolean inverse, int P, int g){long[] dst = Arrays.copyOf(src, n);int h = Integer.numberOfTrailingZeros(n);long K = Integer.highestOneBit(P)<<1;int H = Long.numberOfTrailingZeros(K)*2;long M = K*K/P;long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);long[] wws = new long[1<<h-1];long[] ws = new long[1<<h-1];long w = 1;for(int k = 0;k < 1<<h-1;k++){wws[k] = (w<<32)/P;ws[k] = w;w = modh(w*dw, M, H, P);}for(int i = 0;i < h;i++){for(int j = 0;j < 1<<i;j++){for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){long ndsts = dst[s] + dst[t];if(ndsts >= 2*P)ndsts -= 2*P;long T = dst[s] - dst[t] + 2*P;long Q = wws[k]*T>>>32;dst[s] = ndsts;dst[t] = ws[k]*T-Q*P&(1L<<32)-1;}}// dw = dw * dw % P;if(i < h-1){for(int k = 0;k < 1<<h-i-2;k++){wws[k] = wws[k*2];ws[k] = ws[k*2];}}}for(int i = 0;i < n;i++){if(dst[i] >= P)dst[i] -= P;}for(int i = 0;i < n;i++){int rev = Integer.reverse(i)>>>-h;if(i < rev){long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;}}if(inverse){long in = invl(n, P);for(int i = 0;i < n;i++){dst[i] = modh(dst[i] * in, M, H, P);}}return dst;}static final long mask = (1L<<31)-1;public static long modh(long a, long M, int h, int mod){long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod;return r < mod ? r : r-mod;}private static long[] garnerPrepare(int[] m){int n = m.length;assert n == m.length;if(n == 0)return new long[0];long[] gamma = new long[n];for(int k = 1;k < n;k++){long prod = 1;for(int i = 0;i < k;i++){prod = prod * m[i] % m[k];}gamma[k] = invl(prod, m[k]);}return gamma;}private static long[] garnerBatch(int[] u, int[] m, long[] gamma){int n = u.length;assert n == m.length;long[] v = new long[n];v[0] = u[0];for(int k = 1;k < n;k++){long temp = v[k-1];for(int j = k-2;j >= 0;j--){temp = (temp * m[j] + v[j]) % m[k];}v[k] = (u[k] - temp) * gamma[k] % m[k];if(v[k] < 0)v[k] += m[k];}return v;}private static long pow(long a, long n, long mod) {// a %= mod;long ret = 1;int x = 63 - Long.numberOfLeadingZeros(n);for (; x >= 0; x--) {ret = ret * ret % mod;if (n << 63 - x < 0)ret = ret * a % mod;}return ret;}private static long invl(long a, long mod) {long b = mod;long p = 1, q = 0;while (b > 0) {long c = a / b;long d;d = a;a = b;b = d % b;d = p;p = q;q = d - c * q;}return p < 0 ? p + mod : p;}public static int[] sieveEratosthenes(int n) {if (n <= 32) {int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };for (int i = 0; i < primes.length; i++) {if (n < primes[i]) {return Arrays.copyOf(primes, i);}}return primes;}int u = n + 32;double lu = Math.log(u);int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];ret[0] = 2;int pos = 1;int[] isnp = new int[(n + 1) / 32 / 2 + 1];int sup = (n + 1) / 32 / 2 + 1;int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };for (int tp : tprimes) {ret[pos++] = tp;int[] ptn = new int[tp];for (int i = (tp - 3) / 2; i < tp << 5; i += tp)ptn[i >> 5] |= 1 << (i & 31);for (int j = 0; j < sup; j += tp) {for (int i = 0; i < tp && i + j < sup; i++) {isnp[j + i] |= ptn[i];}}}// 3,5,7// 2x+3=nint[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17,9, 6, 16, 5, 15, 14 };int h = n / 2;for (int i = 0; i < sup; i++) {for (int j = ~isnp[i]; j != 0; j &= j - 1) {int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];int p = 2 * pp + 3;if (p > n)break;ret[pos++] = p;if ((long) p * p > n)continue;for (int q = (p * p - 3) / 2; q <= h; q += p)isnp[q >> 5] |= 1 << q;}}return Arrays.copyOf(ret, pos);}void run() throws Exception{is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());out = new PrintWriter(System.out);long s = System.currentTimeMillis();solve();out.flush();if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");// Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){// @Override// public void run() {// long s = System.currentTimeMillis();// solve();// out.flush();// if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");// }// };// t.start();// t.join();}public static void main(String[] args) throws Exception { new D().run(); }private byte[] inbuf = new byte[1024];public int lenbuf = 0, ptrbuf = 0;private int readByte(){if(lenbuf == -1)throw new InputMismatchException();if(ptrbuf >= lenbuf){ptrbuf = 0;try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }if(lenbuf <= 0)return -1;}return inbuf[ptrbuf++];}private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }private double nd() { return Double.parseDouble(ns()); }private char nc() { return (char)skip(); }private String ns(){int b = skip();StringBuilder sb = new StringBuilder();while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')sb.appendCodePoint(b);b = readByte();}return sb.toString();}private char[] ns(int n){char[] buf = new char[n];int b = skip(), p = 0;while(p < n && !(isSpaceChar(b))){buf[p++] = (char)b;b = readByte();}return n == p ? buf : Arrays.copyOf(buf, p);}private int[] na(int n){int[] a = new int[n];for(int i = 0;i < n;i++)a[i] = ni();return a;}private long[] nal(int n){long[] a = new long[n];for(int i = 0;i < n;i++)a[i] = nl();return a;}private char[][] nm(int n, int m) {char[][] map = new char[n][];for(int i = 0;i < n;i++)map[i] = ns(m);return map;}private int[][] nmi(int n, int m) {int[][] map = new int[n][];for(int i = 0;i < n;i++)map[i] = na(m);return map;}private int ni() { return (int)nl(); }private long nl(){long num = 0;int b;boolean minus = false;while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));if(b == '-'){minus = true;b = readByte();}while(true){if(b >= '0' && b <= '9'){num = num * 10 + (b - '0');}else{return minus ? -num : num;}b = readByte();}}private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }}